If the average of five numbers is 20 and four numbers are 18, 20, 22, and 21, what is the fifth number?

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Multiple Choice

If the average of five numbers is 20 and four numbers are 18, 20, 22, and 21, what is the fifth number?

Explanation:
To find the missing number, use that the total sum of all five numbers equals the average times the count. Here, average is 20 and there are 5 numbers, so the total sum is 20 × 5 = 100. The four given numbers add up to 18 + 20 + 22 + 21 = 81. The fifth number must bring the total to 100, so it is 100 − 81 = 19. Only 19 gives the required total; other values would not maintain the average of 20. The missing number is 19.

To find the missing number, use that the total sum of all five numbers equals the average times the count. Here, average is 20 and there are 5 numbers, so the total sum is 20 × 5 = 100. The four given numbers add up to 18 + 20 + 22 + 21 = 81. The fifth number must bring the total to 100, so it is 100 − 81 = 19. Only 19 gives the required total; other values would not maintain the average of 20. The missing number is 19.

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